Path: news.mathworks.com!not-for-mail
From: <HIDDEN>
Newsgroups: comp.soft-sys.matlab
Subject: Re: why the sigma of symmetrical svd for a real symmetric matrix is negative?
Date: Thu, 27 Dec 2012 04:39:09 +0000 (UTC)
Organization: The MathWorks, Inc.
Lines: 9
Message-ID: <kbgjdd$bao$1@newscl01ah.mathworks.com>
References: <kbgbi5$g5n$1@newscl01ah.mathworks.com>
Reply-To: <HIDDEN>
NNTP-Posting-Host: www-05-blr.mathworks.com
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
X-Trace: newscl01ah.mathworks.com 1356583149 11608 172.30.248.37 (27 Dec 2012 04:39:09 GMT)
X-Complaints-To: news@mathworks.com
NNTP-Posting-Date: Thu, 27 Dec 2012 04:39:09 +0000 (UTC)
X-Newsreader: MATLAB Central Newsreader 1187260
Xref: news.mathworks.com comp.soft-sys.matlab:785455

"Rick" wrote in message <kbgbi5$g5n$1@newscl01ah.mathworks.com>...
>  as we know,  for a real symmetric matrix A, A, there exists a singular value decomposition as A=USU',  and S should be a rectangular diagonal matrix with nonnegative real numbers on the diagonal. But when I use the command schur(),
> it seems that S appears negative real numbers on the diagonal as the following. Is there any problem?
 - - - - - - - - - -
  Unless your A matrix is positive definite there is no reason its singular value and schur decompositions should be the same, and the A you have defined is certainly not positive definite.  In fact all its eigenvalues are negative.  Check the Wikipedia site:

 http://en.wikipedia.org/wiki/Schur_decomposition

Roger Stafford